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2007


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Machine Learning of Motor Skills for Robotics

Peters, J.

University of Southern California, Los Angeles, CA, USA, University of Southern California, Los Angeles, CA, USA, 2007, clmc (phdthesis)

Abstract
Autonomous robots that can assist humans in situations of daily life have been a long standing vision of robotics, artificial intelligence, and cognitive sciences. A first step towards this goal is to create robots that can accomplish a multitude of different tasks, triggered by environmental context or higher level instruction. Early approaches to this goal during the heydays of artificial intelligence research in the late 1980s, however, made it clear that an approach purely based on reasoning and human insights would not be able to model all the perceptuomotor tasks that a robot should fulfill. Instead, new hope was put in the growing wake of machine learning that promised fully adaptive control algorithms which learn both by observation and trial-and-error. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics, and usually scaling was only achieved in precisely pre-structured domains. In this thesis, we investigate the ingredients for a general approach to motor skill learning in order to get one step closer towards human-like performance. For doing so, we study two major components for such an approach, i.e., firstly, a theoretically well-founded general approach to representing the required control structures for task representation and execution and, secondly, appropriate learning algorithms which can be applied in this setting. As a theoretical foundation, we first study a general framework to generate control laws for real robots with a particular focus on skills represented as dynamical systems in differential constraint form. We present a point-wise optimal control framework resulting from a generalization of Gauss' principle and show how various well-known robot control laws can be derived by modifying the metric of the employed cost function. The framework has been successfully applied to task space tracking control for holonomic systems for several different metrics on the anthropomorphic SARCOS Master Arm. In order to overcome the limiting requirement of accurate robot models, we first employ learning methods to find learning controllers for task space control. However, when learning to execute a redundant control problem, we face the general problem of the non-convexity of the solution space which can force the robot to steer into physically impossible configurations if supervised learning methods are employed without further consideration. This problem can be resolved using two major insights, i.e., the learning problem can be treated as locally convex and the cost function of the analytical framework can be used to ensure global consistency. Thus, we derive an immediate reinforcement learning algorithm from the expectation-maximization point of view which leads to a reward-weighted regression technique. This method can be used both for operational space control as well as general immediate reward reinforcement learning problems. We demonstrate the feasibility of the resulting framework on the problem of redundant end-effector tracking for both a simulated 3 degrees of freedom robot arm as well as for a simulated anthropomorphic SARCOS Master Arm. While learning to execute tasks in task space is an essential component to a general framework to motor skill learning, learning the actual task is of even higher importance, particularly as this issue is more frequently beyond the abilities of analytical approaches than execution. We focus on the learning of elemental tasks which can serve as the "building blocks of movement generation", called motor primitives. Motor primitives are parameterized task representations based on splines or nonlinear differential equations with desired attractor properties. While imitation learning of parameterized motor primitives is a relatively well-understood problem, the self-improvement by interaction of the system with the environment remains a challenging problem, tackled in the fourth chapter of this thesis. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and outline both established and novel algorithms for the gradient-based improvement of parameterized policies. We compare these algorithms in the context of motor primitive learning, and show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm. In conclusion, in this thesis, we have contributed a general framework for analytically computing robot control laws which can be used for deriving various previous control approaches and serves as foundation as well as inspiration for our learning algorithms. We have introduced two classes of novel reinforcement learning methods, i.e., the Natural Actor-Critic and the Reward-Weighted Regression algorithm. These algorithms have been used in order to replace the analytical components of the theoretical framework by learned representations. Evaluations have been performed on both simulated and real robot arms.

[BibTex]

2007

[BibTex]


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Reinforcement learning by reward-weighted regression for operational space control

Peters, J., Schaal, S.

In Proceedings of the 24th Annual International Conference on Machine Learning, pages: 745-750, ICML, 2007, clmc (inproceedings)

Abstract
Many robot control problems of practical importance, including operational space control, can be reformulated as immediate reward reinforcement learning problems. However, few of the known optimization or reinforcement learning algorithms can be used in online learning control for robots, as they are either prohibitively slow, do not scale to interesting domains of complex robots, or require trying out policies generated by random search, which are infeasible for a physical system. Using a generalization of the EM-base reinforcement learning framework suggested by Dayan & Hinton, we reduce the problem of learning with immediate rewards to a reward-weighted regression problem with an adaptive, integrated reward transformation for faster convergence. The resulting algorithm is efficient, learns smoothly without dangerous jumps in solution space, and works well in applications of complex high degree-of-freedom robots.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Policy gradient methods for machine learning

Peters, J., Theodorou, E., Schaal, S.

In Proceedings of the 14th INFORMS Conference of the Applied Probability Society, pages: 97-98, Eindhoven, Netherlands, July 9-11, 2007, 2007, clmc (inproceedings)

Abstract
We present an in-depth survey of policy gradient methods as they are used in the machine learning community for optimizing parameterized, stochastic control policies in Markovian systems with respect to the expected reward. Despite having been developed separately in the reinforcement learning literature, policy gradient methods employ likelihood ratio gradient estimators as also suggested in the stochastic simulation optimization community. It is well-known that this approach to policy gradient estimation traditionally suffers from three drawbacks, i.e., large variance, a strong dependence on baseline functions and a inefficient gradient descent. In this talk, we will present a series of recent results which tackles each of these problems. The variance of the gradient estimation can be reduced significantly through recently introduced techniques such as optimal baselines, compatible function approximations and all-action gradients. However, as even the analytically obtainable policy gradients perform unnaturally slow, it required the step from ÔvanillaÕ policy gradient methods towards natural policy gradients in order to overcome the inefficiency of the gradient descent. This development resulted into the Natural Actor-Critic architecture which can be shown to be very efficient in application to motor primitive learning for robotics.

[BibTex]

[BibTex]


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Policy Learning for Motor Skills

Peters, J., Schaal, S.

In Proceedings of 14th International Conference on Neural Information Processing (ICONIP), pages: 233-242, (Editors: Ishikawa, M. , K. Doya, H. Miyamoto, T. Yamakawa), 2007, clmc (inproceedings)

Abstract
Policy learning which allows autonomous robots to adapt to novel situations has been a long standing vision of robotics, artificial intelligence, and cognitive sciences. However, to date, learning techniques have yet to fulfill this promise as only few methods manage to scale into the high-dimensional domains of manipulator robotics, or even the new upcoming trend of humanoid robotics, and usually scaling was only achieved in precisely pre-structured domains. In this paper, we investigate the ingredients for a general approach policy learning with the goal of an application to motor skill refinement in order to get one step closer towards human-like performance. For doing so, we study two major components for such an approach, i.e., firstly, we study policy learning algorithms which can be applied in the general setting of motor skill learning, and, secondly, we study a theoretically well-founded general approach to representing the required control structures for task representation and execution.

PDF DOI [BibTex]

PDF DOI [BibTex]


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Reinforcement learning for operational space control

Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Conference on Robotics and Automation, pages: 2111-2116, IEEE Computer Society, ICRA, 2007, clmc (inproceedings)

Abstract
While operational space control is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in complex robots, e.g., humanoid robots. In such cases, learning control methods can offer an interesting alternative to analytical control algorithms. However, the resulting supervised learning problem is ill-defined as it requires to learn an inverse mapping of a usually redundant system, which is well known to suffer from the property of non-convexity of the solution space, i.e., the learning system could generate motor commands that try to steer the robot into physically impossible configurations. The important insight that many operational space control algorithms can be reformulated as optimal control problems, however, allows addressing this inverse learning problem in the framework of reinforcement learning. However, few of the known optimization or reinforcement learning algorithms can be used in online learning control for robots, as they are either prohibitively slow, do not scale to interesting domains of complex robots, or require trying out policies generated by random search, which are infeasible for a physical system. Using a generalization of the EM-based reinforcement learning framework suggested by Dayan & Hinton, we reduce the problem of learning with immediate rewards to a reward-weighted regression problem with an adaptive, integrated reward transformation for faster convergence. The resulting algorithm is efficient, learns smoothly without dangerous jumps in solution space, and works well in applications of complex high degree-of-freedom robots.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Relative Entropy Policy Search

Peters, J.

CLMC Technical Report: TR-CLMC-2007-2, Computational Learning and Motor Control Lab, Los Angeles, CA, 2007, clmc (techreport)

Abstract
This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems.

PDF link (url) [BibTex]

PDF link (url) [BibTex]


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Less Conservative Polytopic LPV Models for Charge Control by Combining Parameter Set Mapping and Set Intersection

Kwiatkowski, A., Trimpe, S., Werner, H.

In Proceedings of the 46th IEEE Conference on Decision and Control, 2007 (inproceedings)

DOI [BibTex]

DOI [BibTex]


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Using reward-weighted regression for reinforcement learning of task space control

Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, pages: 262-267, Honolulu, Hawaii, April 1-5, 2007, 2007, clmc (inproceedings)

Abstract
In this paper, we evaluate different versions from the three main kinds of model-free policy gradient methods, i.e., finite difference gradients, `vanilla' policy gradients and natural policy gradients. Each of these methods is first presented in its simple form and subsequently refined and optimized. By carrying out numerous experiments on the cart pole regulator benchmark we aim to provide a useful baseline for future research on parameterized policy search algorithms. Portable C++ code is provided for both plant and algorithms; thus, the results in this paper can be reevaluated, reused and new algorithms can be inserted with ease.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Evaluation of Policy Gradient Methods and Variants on the Cart-Pole Benchmark

Riedmiller, M., Peters, J., Schaal, S.

In Proceedings of the 2007 IEEE International Symposium on Approximate Dynamic Programming and Reinforcement Learning, pages: 254-261, ADPRL, 2007, clmc (inproceedings)

Abstract
In this paper, we evaluate different versions from the three main kinds of model-free policy gradient methods, i.e., finite difference gradients, `vanilla' policy gradients and natural policy gradients. Each of these methods is first presented in its simple form and subsequently refined and optimized. By carrying out numerous experiments on the cart pole regulator benchmark we aim to provide a useful baseline for future research on parameterized policy search algorithms. Portable C++ code is provided for both plant and algorithms; thus, the results in this paper can be reevaluated, reused and new algorithms can be inserted with ease.

PDF [BibTex]

PDF [BibTex]


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Uncertain 3D Force Fields in Reaching Movements: Do Humans Favor Robust or Average Performance?

Mistry, M., Theodorou, E., Hoffmann, H., Schaal, S.

In Abstracts of the 37th Meeting of the Society of Neuroscience, 2007, clmc (inproceedings)

PDF [BibTex]

PDF [BibTex]


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Applying the episodic natural actor-critic architecture to motor primitive learning

Peters, J., Schaal, S.

In Proceedings of the 2007 European Symposium on Artificial Neural Networks (ESANN), Bruges, Belgium, April 25-27, 2007, clmc (inproceedings)

Abstract
In this paper, we investigate motor primitive learning with the Natural Actor-Critic approach. The Natural Actor-Critic consists out of actor updates which are achieved using natural stochastic policy gradients while the critic obtains the natural policy gradient by linear regression. We show that this architecture can be used to learn the Òbuilding blocks of movement generationÓ, called motor primitives. Motor primitives are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. We show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm.

link (url) [BibTex]

link (url) [BibTex]


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The new robotics - towards human-centered machines

Schaal, S.

HFSP Journal Frontiers of Interdisciplinary Research in the Life Sciences, 1(2):115-126, 2007, clmc (article)

Abstract
Research in robotics has moved away from its primary focus on industrial applications. The New Robotics is a vision that has been developed in past years by our own university and many other national and international research instiutions and addresses how increasingly more human-like robots can live among us and take over tasks where our current society has shortcomings. Elder care, physical therapy, child education, search and rescue, and general assistance in daily life situations are some of the examples that will benefit from the New Robotics in the near future. With these goals in mind, research for the New Robotics has to embrace a broad interdisciplinary approach, ranging from traditional mathematical issues of robotics to novel issues in psychology, neuroscience, and ethics. This paper outlines some of the important research problems that will need to be resolved to make the New Robotics a reality.

link (url) [BibTex]

link (url) [BibTex]


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A computational model of human trajectory planning based on convergent flow fields

Hoffman, H., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov. 3-7, 2007, clmc (inproceedings)

Abstract
A popular computational model suggests that smooth reaching movements are generated in humans by minimizing a difference vector between hand and target in visual coordinates (Shadmehr and Wise, 2005). To achieve such a task, the optimal joint accelerations may be pre-computed. However, this pre-planning is inflexible towards perturbations of the limb, and there is strong evidence that reaching movements can be modified on-line at any moment during the movement. Thus, next-state planning models (Bullock and Grossberg, 1988) have been suggested that compute the current control command from a function of the goal state such that the overall movement smoothly converges to the goal (see Shadmehr and Wise (2005) for an overview). So far, these models have been restricted to simple point-to-point reaching movements with (approximately) straight trajectories. Here, we present a computational model for learning and executing arbitrary trajectories that combines ideas from pattern generation with dynamic systems and the observation of convergent force fields, which control a frog leg after spinal stimulation (Giszter et al., 1993). In our model, we incorporate the following two observations: first, the orientation of vectors in a force field is invariant over time, but their amplitude is modulated by a time-varying function, and second, two force fields add up when stimulated simultaneously (Giszter et al., 1993). This addition of convergent force fields varying over time results in a virtual trajectory (a moving equilibrium point) that correlates with the actual leg movement (Giszter et al., 1993). Our next-state planner is a set of differential equations that provide the desired end-effector or joint accelerations using feedback of the current state of the limb. These accelerations can be interpreted as resulting from a damped spring that links the current limb position with a virtual trajectory. This virtual trajectory can be learned to realize any desired limb trajectory and velocity profile, and learning is efficient since the time-modulated sum of convergent force fields equals a sum of weighted basis functions (Gaussian time pulses). Thus, linear algebra is sufficient to compute these weights, which correspond to points on the virtual trajectory. During movement execution, the differential equation corrects automatically for perturbations and brings back smoothly the limb towards the goal. Virtual trajectories can be rescaled and added allowing to build a set of movement primitives to describe movements more complex than previously learned. We demonstrate the potential of the suggested model by learning and generating a wide variety of movements.

[BibTex]

[BibTex]


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A Computational Model of Arm Trajectory Modification Using Dynamic Movement Primitives

Mohajerian, P., Hoffmann, H., Mistry, M., Schaal, S.

In Abstracts of the 37st Meeting of the Society of Neuroscience, San Diego, CA, Nov 3-7, 2007, clmc (inproceedings)

Abstract
Several scientists used a double-step target-displacement protocol to investigate how an unexpected upcoming new target modifies ongoing discrete movements. Interesting observations are the initial direction of the movement, the spatial path of the movement to the second target, and the amplification of the speed in the second movement. Experimental data show that the above properties are influenced by the movement reaction time and the interstimulus interval between the onset of the first and second target. Hypotheses in the literature concerning the interpretation of the observed data include a) the second movement is superimposed on the first movement (Henis and Flash, 1995), b) the first movement is aborted and the second movement is planned to smoothly connect the current state of the arm with the new target (Hoff and Arbib, 1992), c) the second movement is initiated by a new control signal that replaces the first movement's control signal, but does not take the state of the system into account (Flanagan et al., 1993), and (d) the second movement is initiated by a new goal command, but the control structure stays unchanged, and feed-back from the current state is taken into account (Hoff and Arbib, 1993). We investigate target switching from the viewpoint of Dynamic Movement Primitives (DMPs). DMPs are trajectory planning units that are formalized as stable nonlinear attractor systems (Ijspeert et al., 2002). They are a useful framework for biological motor control as they are highly flexible in creating complex rhythmic and discrete behaviors that can quickly adapt to the inevitable perturbations of dynamically changing, stochastic environments. In this model, target switching is accomplished simply by updating the target input to the discrete movement primitive for reaching. The reaching trajectory in this model can be straight or take any other route; in contrast, the Hoff and Arbib (1993) model is restricted to straight reaching movement plans. In the present study, we use DMPs to reproduce in simulation a large number of target-switching experimental data from the literature and to show that online correction and the observed target switching phenomena can be accomplished by changing the goal state of an on-going DMP, without the need to switch to different movement primitives or to re-plan the movement. :

PDF [BibTex]

PDF [BibTex]


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Inverse dynamics control with floating base and constraints

Nakanishi, J., Mistry, M., Schaal, S.

In International Conference on Robotics and Automation (ICRA2007), pages: 1942-1947, Rome, Italy, April 10-14, 2007, clmc (inproceedings)

Abstract
In this paper, we address the issues of compliant control of a robot under contact constraints with a goal of using joint space based pattern generators as movement primitives, as often considered in the studies of legged locomotion and biological motor control. For this purpose, we explore inverse dynamics control of constrained dynamical systems. When the system is overconstrained, it is not straightforward to formulate an inverse dynamics control law since the problem becomes an ill-posed one, where infinitely many combinations of joint torques are possible to achieve the desired joint accelerations. The goal of this paper is to develop a general and computationally efficient inverse dynamics algorithm for a robot with a free floating base and constraints. We suggest an approximate way of computing inverse dynamics algorithm by treating constraint forces computed with a Lagrange multiplier method as simply external forces based on FeatherstoneÕs floating base formulation of inverse dynamics. We present how all the necessary quantities to compute our controller can be efficiently extracted from FeatherstoneÕs spatial notation of robot dynamics. We evaluate the effectiveness of the suggested approach on a simulated biped robot model.

link (url) [BibTex]

link (url) [BibTex]


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Dynamics systems vs. optimal control ? a unifying view

Schaal, S, Mohajerian, P., Ijspeert, A.

In Progress in Brain Research, (165):425-445, 2007, clmc (inbook)

Abstract
In the past, computational motor control has been approached from at least two major frameworks: the dynamic systems approach and the viewpoint of optimal control. The dynamic system approach emphasizes motor control as a process of self-organization between an animal and its environment. Nonlinear differential equations that can model entrainment and synchronization behavior are among the most favorable tools of dynamic systems modelers. In contrast, optimal control approaches view motor control as the evolutionary or development result of a nervous system that tries to optimize rather general organizational principles, e.g., energy consumption or accurate task achievement. Optimal control theory is usually employed to develop appropriate theories. Interestingly, there is rather little interaction between dynamic systems and optimal control modelers as the two approaches follow rather different philosophies and are often viewed as diametrically opposing. In this paper, we develop a computational approach to motor control that offers a unifying modeling framework for both dynamic systems and optimal control approaches. In discussions of several behavioral experiments and some theoretical and robotics studies, we demonstrate how our computational ideas allow both the representation of self-organizing processes and the optimization of movement based on reward criteria. Our modeling framework is rather simple and general, and opens opportunities to revisit many previous modeling results from this novel unifying view.

link (url) [BibTex]

link (url) [BibTex]


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Kernel carpentry for onlne regression using randomly varying coefficient model

Edakunni, N. U., Schaal, S., Vijayakumar, S.

In Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India: Jan. 6-12, 2007, clmc (inproceedings)

Abstract
We present a Bayesian formulation of locally weighted learning (LWL) using the novel concept of a randomly varying coefficient model. Based on this, we propose a mechanism for multivariate non-linear regression using spatially localised linear models that learns completely independent of each other, uses only local information and adapts the local model complexity in a data driven fashion. We derive online updates for the model parameters based on variational Bayesian EM. The evaluation of the proposed algorithm against other state-of-the-art methods reveal the excellent, robust generalization performance beside surprisingly efficient time and space complexity properties. This paper, for the first time, brings together the computational efficiency and the adaptability of Õnon-competitiveÕ locally weighted learning schemes and the modeling guarantees of the Bayesian formulation.

link (url) [BibTex]

link (url) [BibTex]


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A robust quadruped walking gait for traversing rough terrain

Pongas, D., Mistry, M., Schaal, S.

In International Conference on Robotics and Automation (ICRA2007), pages: 1474-1479, Rome, April 10-14, 2007, 2007, clmc (inproceedings)

Abstract
Legged locomotion excels when terrains become too rough for wheeled systems or open-loop walking pattern generators to succeed, i.e., when accurate foot placement is of primary importance in successfully reaching the task goal. In this paper we address the scenario where the rough terrain is traversed with a static walking gait, and where for every foot placement of a leg, the location of the foot placement was selected irregularly by a planning algorithm. Our goal is to adjust a smooth walking pattern generator with the selection of every foot placement such that the COG of the robot follows a stable trajectory characterized by a stability margin relative to the current support triangle. We propose a novel parameterization of the COG trajectory based on the current position, velocity, and acceleration of the four legs of the robot. This COG trajectory has guaranteed continuous velocity and acceleration profiles, which leads to continuous velocity and acceleration profiles of the leg movement, which is ideally suited for advanced model-based controllers. Pitch, yaw, and ground clearance of the robot are easily adjusted automatically under any terrain situation. We evaluate our gait generation technique on the Little-Dog quadruped robot when traversing complex rocky and sloped terrains.

link (url) [BibTex]

link (url) [BibTex]


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Bayesian Nonparametric Regression with Local Models

Ting, J., Schaal, S.

In Workshop on Robotic Challenges for Machine Learning, NIPS 2007, 2007, clmc (inproceedings)

[BibTex]

[BibTex]


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Learning an Outlier-Robust Kalman Filter

Ting, J., Theodorou, E., Schaal, S.

CLMC Technical Report: TR-CLMC-2007-1, Los Angeles, CA, 2007, clmc (techreport)

Abstract
We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user. Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers. The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue. However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step?s state. Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics. We evaluate our Kalman filter algorithm on data from a robotic dog.

PDF [BibTex]

PDF [BibTex]


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Task space control with prioritization for balance and locomotion

Mistry, M., Nakanishi, J., Schaal, S.

In IEEE International Conference on Intelligent Robotics Systems (IROS 2007), San Diego, CA: Oct. 29 Ð Nov. 2, 2007, clmc (inproceedings)

Abstract
This paper addresses locomotion with active balancing, via task space control with prioritization. The center of gravity (COG) and foot of the swing leg are treated as task space control points. Floating base inverse kinematics with constraints is employed, thereby allowing for a mobile platform suitable for locomotion. Different techniques of task prioritization are discussed and we clarify differences and similarities of previous suggested work. Varying levels of prioritization for control are examined with emphasis on singularity robustness and the negative effects of constraint switching. A novel controller for task space control of balance and locomotion is developed which attempts to address singularity robustness, while minimizing discontinuities created by constraint switching. Controllers are evaluated using a quadruped robot simulator engaging in a locomotion task.

link (url) [BibTex]

link (url) [BibTex]

2006


Molecular Modeling for the BioPrint Pharmaco-informatics Platform
Molecular Modeling for the BioPrint Pharmaco-informatics Platform

Berenz, V., Tillier, F., Barbosa, F., Boryeu, M., Horvath, D., Froloff, N.

2006 (poster)

[BibTex]

2006

[BibTex]


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Learning operational space control

Peters, J., Schaal, S.

In Robotics: Science and Systems II (RSS 2006), pages: 255-262, (Editors: Gaurav S. Sukhatme and Stefan Schaal and Wolfram Burgard and Dieter Fox), Cambridge, MA: MIT Press, RSS , 2006, clmc (inproceedings)

Abstract
While operational space control is of essential importance for robotics and well-understood from an analytical point of view, it can be prohibitively hard to achieve accurate control in face of modeling errors, which are inevitable in complex robots, e.g., humanoid robots. In such cases, learning control methods can offer an interesting alternative to analytical control algorithms. However, the resulting learning problem is ill-defined as it requires to learn an inverse mapping of a usually redundant system, which is well known to suffer from the property of non-covexity of the solution space, i.e., the learning system could generate motor commands that try to steer the robot into physically impossible configurations. A first important insight for this paper is that, nevertheless, a physically correct solution to the inverse problem does exits when learning of the inverse map is performed in a suitable piecewise linear way. The second crucial component for our work is based on a recent insight that many operational space controllers can be understood in terms of a constraint optimal control problem. The cost function associated with this optimal control problem allows us to formulate a learning algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller. From the view of machine learning, the learning problem corresponds to a reinforcement learning problem that maximizes an immediate reward and that employs an expectation-maximization policy search algorithm. Evaluations on a three degrees of freedom robot arm illustrate the feasability of our suggested approach.

link (url) [BibTex]

link (url) [BibTex]


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Reinforcement Learning for Parameterized Motor Primitives

Peters, J., Schaal, S.

In Proceedings of the 2006 International Joint Conference on Neural Networks, pages: 73-80, IJCNN, 2006, clmc (inproceedings)

Abstract
One of the major challenges in both action generation for robotics and in the understanding of human motor control is to learn the "building blocks of movement generation", called motor primitives. Motor primitives, as used in this paper, are parameterized control policies such as splines or nonlinear differential equations with desired attractor properties. While a lot of progress has been made in teaching parameterized motor primitives using supervised or imitation learning, the self-improvement by interaction of the system with the environment remains a challenging problem. In this paper, we evaluate different reinforcement learning approaches for improving the performance of parameterized motor primitives. For pursuing this goal, we highlight the difficulties with current reinforcement learning methods, and outline both established and novel algorithms for the gradient-based improvement of parameterized policies. We compare these algorithms in the context of motor primitive learning, and show that our most modern algorithm, the Episodic Natural Actor-Critic outperforms previous algorithms by at least an order of magnitude. We demonstrate the efficiency of this reinforcement learning method in the application of learning to hit a baseball with an anthropomorphic robot arm.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Policy gradient methods for robotics

Peters, J., Schaal, S.

In Proceedings of the IEEE International Conference on Intelligent Robotics Systems, pages: 2219-2225, IROS, 2006, clmc (inproceedings)

Abstract
The aquisition and improvement of motor skills and control policies for robotics from trial and error is of essential importance if robots should ever leave precisely pre-structured environments. However, to date only few existing reinforcement learning methods have been scaled into the domains of highdimensional robots such as manipulator, legged or humanoid robots. Policy gradient methods remain one of the few exceptions and have found a variety of applications. Nevertheless, the application of such methods is not without peril if done in an uninformed manner. In this paper, we give an overview on learning with policy gradient methods for robotics with a strong focus on recent advances in the field. We outline previous applications to robotics and show how the most recently developed methods can significantly improve learning performance. Finally, we evaluate our most promising algorithm in the application of hitting a baseball with an anthropomorphic arm.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Statistical Learning of LQG controllers

Theodorou, E.

Technical Report-2006-1, Computational Action and Vision Lab University of Minnesota, 2006, clmc (techreport)

PDF [BibTex]

PDF [BibTex]


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Approximate nearest neighbor regression in very high dimensions

Vijayakumar, S., DSouza, A., Schaal, S.

In Nearest-Neighbor Methods in Learning and Vision, pages: 103-142, (Editors: Shakhnarovich, G.;Darrell, T.;Indyk, P.), Cambridge, MA: MIT Press, 2006, clmc (inbook)

link (url) [BibTex]

link (url) [BibTex]

2005


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Composite adaptive control with locally weighted statistical learning

Nakanishi, J., Farrell, J. A., Schaal, S.

Neural Networks, 18(1):71-90, January 2005, clmc (article)

Abstract
This paper introduces a provably stable learning adaptive control framework with statistical learning. The proposed algorithm employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and the working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using a nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized on-line. Inspired by composite adaptive control methods, the proposed learning adaptive control algorithm uses both the tracking error and the estimation error to update the parameters. We first discuss statistical learning of nonlinear functions, and motivate our choice of the locally weighted learning framework. Second, we begin with a class of first order SISO systems for theoretical development of our learning adaptive control framework, and present a stability proof including a parameter projection method that is needed to avoid potential singularities during adaptation. Then, we generalize our adaptive controller to higher order SISO systems, and discuss further extension to MIMO problems. Finally, we evaluate our theoretical control framework in numerical simulations to illustrate the effectiveness of the proposed learning adaptive controller for rapid convergence and high accuracy of control.

link (url) [BibTex]

2005

link (url) [BibTex]


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Natural Actor-Critic

Peters, J., Vijayakumar, S., Schaal, S.

In Proceedings of the 16th European Conference on Machine Learning, 3720, pages: 280-291, (Editors: Gama, J.;Camacho, R.;Brazdil, P.;Jorge, A.;Torgo, L.), Springer, ECML, 2005, clmc (inproceedings)

Abstract
This paper investigates a novel model-free reinforcement learning architecture, the Natural Actor-Critic. The actor updates are based on stochastic policy gradients employing AmariÕs natural gradient approach, while the critic obtains both the natural policy gradient and additional parameters of a value function simultaneously by linear regres- sion. We show that actor improvements with natural policy gradients are particularly appealing as these are independent of coordinate frame of the chosen policy representation, and can be estimated more efficiently than regular policy gradients. The critic makes use of a special basis function parameterization motivated by the policy-gradient compatible function approximation. We show that several well-known reinforcement learning methods such as the original Actor-Critic and BradtkeÕs Linear Quadratic Q-Learning are in fact Natural Actor-Critic algorithms. Em- pirical evaluations illustrate the effectiveness of our techniques in com- parison to previous methods, and also demonstrate their applicability for learning control on an anthropomorphic robot arm.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Comparative experiments on task space control with redundancy resolution

Nakanishi, J., Cory, R., Mistry, M., Peters, J., Schaal, S.

In Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 3901-3908, Edmonton, Alberta, Canada, Aug. 2-6, IROS, 2005, clmc (inproceedings)

Abstract
Understanding the principles of motor coordination with redundant degrees of freedom still remains a challenging problem, particularly for new research in highly redundant robots like humanoids. Even after more than a decade of research, task space control with redundacy resolution still remains an incompletely understood theoretical topic, and also lacks a larger body of thorough experimental investigation on complex robotic systems. This paper presents our first steps towards the development of a working redundancy resolution algorithm which is robust against modeling errors and unforeseen disturbances arising from contact forces. To gain a better understanding of the pros and cons of different approaches to redundancy resolution, we focus on a comparative empirical evaluation. First, we review several redundancy resolution schemes at the velocity, acceleration and torque levels presented in the literature in a common notational framework and also introduce some new variants of these previous approaches. Second, we present experimental comparisons of these approaches on a seven-degree-of-freedom anthropomorphic robot arm. Surprisingly, one of our simplest algorithms empirically demonstrates the best performance, despite, from a theoretical point, the algorithm does not share the same beauty as some of the other methods. Finally, we discuss practical properties of these control algorithms, particularly in light of inevitable modeling errors of the robot dynamics.

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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A model of smooth pursuit based on learning of the target dynamics using only retinal signals

Shibata, T., Tabata, H., Schaal, S., Kawato, M.

Neural Networks, 18, pages: 213-225, 2005, clmc (article)

Abstract
While the predictive nature of the primate smooth pursuit system has been evident through several behavioural and neurophysiological experiments, few models have attempted to explain these results comprehensively. The model we propose in this paper in line with previous models employing optimal control theory; however, we hypothesize two new issues: (1) the medical superior temporal (MST) area in the cerebral cortex implements a recurrent neural network (RNN) in order to predict the current or future target velocity, and (2) a forward model of the target motion is acquired by on-line learning. We use stimulation studies to demonstrate how our new model supports these hypotheses.

link (url) [BibTex]

link (url) [BibTex]


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Linear and Nonlinear Estimation models applied to Hemodynamic Model

Theodorou, E.

Technical Report-2005-1, Computational Action and Vision Lab University of Minnesota, 2005, clmc (techreport)

Abstract
The relation between BOLD signal and neural activity is still poorly understood. The Gaussian Linear Model known as GLM is broadly used in many fMRI data analysis for recovering the underlying neural activity. Although GLM has been proved to be a really useful tool for analyzing fMRI data it can not be used for describing the complex biophysical process of neural metabolism. In this technical report we make use of a system of Stochastic Differential Equations that is based on Buxton model [1] for describing the underlying computational principles of hemodynamic process. Based on this SDE we built a Kalman Filter estimator so as to estimate the induced neural signal as well as the blood inflow under physiologic and sensor noise. The performance of Kalman Filter estimator is investigated under different physiologic noise characteristics and measurement frequencies.

PDF [BibTex]

PDF [BibTex]


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Predicting EMG Data from M1 Neurons with Variational Bayesian Least Squares

Ting, J., D’Souza, A., Yamamoto, K., Yoshioka, T., Hoffman, D., Kakei, S., Sergio, L., Kalaska, J., Kawato, M., Strick, P., Schaal, S.

In Advances in Neural Information Processing Systems 18 (NIPS 2005), (Editors: Weiss, Y.;Schölkopf, B.;Platt, J.), Cambridge, MA: MIT Press, Vancouver, BC, Dec. 6-11, 2005, clmc (inproceedings)

Abstract
An increasing number of projects in neuroscience requires the statistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing, or in operating artificial devices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classi-cal linear regression approaches are often numercially too fragile in high dimen-sions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faithfully reconstructed with linear ap-proaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that automatically detects and excludes irrelevant features in the data, and regular-izes against overfitting. In comparison with ordinary least squares, stepwise re-gression, partial least squares, and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of regularization against overfitting, computational efficiency, and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques. As neuroscientific results, our analyses demonstrate that EMG data can be well pre-dicted from M1 neurons, further opening the path for possible real-time inter-faces between brains and machines.

link (url) [BibTex]

link (url) [BibTex]


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Rapbid synchronization and accurate phase-locking of rhythmic motor primitives

Pongas, D., Billard, A., Schaal, S.

In IEEE International Conference on Intelligent Robots and Systems (IROS 2005), pages: 2911-2916, Edmonton, Alberta, Canada, Aug. 2-6, 2005, clmc (inproceedings)

Abstract
Rhythmic movement is ubiquitous in human and animal behavior, e.g., as in locomotion, dancing, swimming, chewing, scratching, music playing, etc. A particular feature of rhythmic movement in biology is the rapid synchronization and phase locking with other rhythmic events in the environment, for instance music or visual stimuli as in ball juggling. In traditional oscillator theories to rhythmic movement generation, synchronization with another signal is relatively slow, and it is not easy to achieve accurate phase locking with a particular feature of the driving stimulus. Using a recently developed framework of dynamic motor primitives, we demonstrate a novel algorithm for very rapid synchronizaton of a rhythmic movement pattern, which can phase lock any feature of the movement to any particulur event in the driving stimulus. As an example application, we demonstrate how an anthropomorphic robot can use imitation learning to acquire a complex rumming pattern and keep it synchronized with an external rhythm generator that changes its frequency over time.

link (url) [BibTex]

link (url) [BibTex]


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Parametric and Non-Parametric approaches for nonlinear tracking of moving objects

Hidaka, Y, Theodorou, E.

Technical Report-2005-1, 2005, clmc (article)

PDF [BibTex]

PDF [BibTex]


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A new methodology for robot control design

Peters, J., Mistry, M., Udwadia, F. E., Schaal, S.

In The 5th ASME International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC 2005), Long Beach, CA, Sept. 24-28, 2005, clmc (inproceedings)

Abstract
Gauss principle of least constraint and its generalizations have provided a useful insights for the development of tracking controllers for mechanical systems (Udwadia,2003). Using this concept, we present a novel methodology for the design of a specific class of robot controllers. With our new framework, we demonstrate that well-known and also several novel nonlinear robot control laws can be derived from this generic framework, and show experimental verifications on a Sarcos Master Arm robot for some of these controllers. We believe that the suggested approach unifies and simplifies the design of optimal nonlinear control laws for robots obeying rigid body dynamics equations, both with or without external constraints, holonomic or nonholonomic constraints, with over-actuation or underactuation, as well as open-chain and closed-chain kinematics.

link (url) [BibTex]

link (url) [BibTex]


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Arm movement experiments with joint space force fields using an exoskeleton robot

Mistry, M., Mohajerian, P., Schaal, S.

In IEEE Ninth International Conference on Rehabilitation Robotics, pages: 408-413, Chicago, Illinois, June 28-July 1, 2005, clmc (inproceedings)

Abstract
A new experimental platform permits us to study a novel variety of issues of human motor control, particularly full 3-D movements involving the major seven degrees-of-freedom (DOF) of the human arm. We incorporate a seven DOF robot exoskeleton, and can minimize weight and inertia through gravity, Coriolis, and inertia compensation, such that subjects' arm movements are largely unaffected by the manipulandum. Torque perturbations can be individually applied to any or all seven joints of the human arm, thus creating novel dynamic environments, or force fields, for subjects to respond and adapt to. Our first study investigates a joint space force field where the shoulder velocity drives a disturbing force in the elbow joint. Results demonstrate that subjects learn to compensate for the force field within about 100 trials, and from the strong presence of aftereffects when removing the field in some randomized catch trials, that an inverse dynamics, or internal model, of the force field is formed by the nervous system. Interestingly, while post-learning hand trajectories return to baseline, joint space trajectories remained changed in response to the field, indicating that besides learning a model of the force field, the nervous system also chose to exploit the space to minimize the effects of the force field on the realization of the endpoint trajectory plan. Further applications for our apparatus include studies in motor system redundancy resolution and inverse kinematics, as well as rehabilitation.

link (url) [BibTex]

link (url) [BibTex]


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A unifying framework for the control of robotics systems

Peters, J., Mistry, M., Udwadia, F. E., Cory, R., Nakanishi, J., Schaal, S.

In IEEE International Conference on Intelligent Robots and Systems (IROS 2005), pages: 1824-1831, Edmonton, Alberta, Canada, Aug. 2-6, 2005, clmc (inproceedings)

Abstract
Recently, [1] suggested to derive tracking controllers for mechanical systems using a generalization of GaussÕ principle of least constraint. This method al-lows us to reformulate control problems as a special class of optimal control. We take this line of reasoning one step further and demonstrate that well-known and also several novel nonlinear robot control laws can be derived from this generic methodology. We show experimental verifications on a Sar-cos Master Arm robot for some of the the derived controllers.We believe that the suggested approach offers a promising unification and simplification of nonlinear control law design for robots obeying rigid body dynamics equa-tions, both with or without external constraints, with over-actuation or under-actuation, as well as open-chain and closed-chain kinematics.

link (url) [BibTex]

link (url) [BibTex]

1999


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Is imitation learning the route to humanoid robots?

Schaal, S.

Trends in Cognitive Sciences, 3(6):233-242, 1999, clmc (article)

Abstract
This review will focus on two recent developments in artificial intelligence and neural computation: learning from imitation and the development of humanoid robots. It will be postulated that the study of imitation learning offers a promising route to gain new insights into mechanisms of perceptual motor control that could ultimately lead to the creation of autonomous humanoid robots. This hope is justified because imitation learning channels research efforts towards three important issues: efficient motor learning, the connection between action and perception, and modular motor control in form of movement primitives. In order to make these points, first, a brief review of imitation learning will be given from the view of psychology and neuroscience. In these fields, representations and functional connections between action and perception have been explored that contribute to the understanding of motor acts of other beings. The recent discovery that some areas in the primate brain are active during both movement perception and execution provided a first idea of the possible neural basis of imitation. Secondly, computational approaches to imitation learning will be described, initially from the perspective of traditional AI and robotics, and then with a focus on neural network models and statistical learning research. Parallels and differences between biological and computational approaches to imitation will be highlighted. The review will end with an overview of current projects that actually employ imitation learning for humanoid robots.

link (url) [BibTex]

1999

link (url) [BibTex]


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Nonparametric regression for learning nonlinear transformations

Schaal, S.

In Prerational Intelligence in Strategies, High-Level Processes and Collective Behavior, 2, pages: 595-621, (Editors: Ritter, H.;Cruse, H.;Dean, J.), Kluwer Academic Publishers, 1999, clmc (inbook)

Abstract
Information processing in animals and artificial movement systems consists of a series of transformations that map sensory signals to intermediate representations, and finally to motor commands. Given the physical and neuroanatomical differences between individuals and the need for plasticity during development, it is highly likely that such transformations are learned rather than pre-programmed by evolution. Such self-organizing processes, capable of discovering nonlinear dependencies between different groups of signals, are one essential part of prerational intelligence. While neural network algorithms seem to be the natural choice when searching for solutions for learning transformations, this paper will take a more careful look at which types of neural networks are actually suited for the requirements of an autonomous learning system. The approach that we will pursue is guided by recent developments in learning theory that have linked neural network learning to well established statistical theories. In particular, this new statistical understanding has given rise to the development of neural network systems that are directly based on statistical methods. One family of such methods stems from nonparametric regression. This paper will compare nonparametric learning with the more widely used parametric counterparts in a non technical fashion, and investigate how these two families differ in their properties and their applicabilities. We will argue that nonparametric neural networks offer a set of characteristics that make them a very promising candidate for on-line learning in autonomous system.

link (url) [BibTex]

link (url) [BibTex]


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Segmentation of endpoint trajectories does not imply segmented control

Sternad, D., Schaal, D.

Experimental Brain Research, 124(1):118-136, 1999, clmc (article)

Abstract
While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, still remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in 3D human drawing movements are re-examined: (1) the stroke-based segmentation hypothesis based on the results that the proportionality coefficient of the 2/3 power law changes discontinuously with each new â??strokeâ?, and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of 3D drawing movements. In two experiments human subjects performed a set of elliptical and figure-8 patterns of different sizes and orientations using their whole arm in 3D. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features as reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.

link (url) [BibTex]

link (url) [BibTex]

1998


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Programmable pattern generators

Schaal, S., Sternad, D.

In 3rd International Conference on Computational Intelligence in Neuroscience, pages: 48-51, Research Triangle Park, NC, Oct. 24-28, October 1998, clmc (inproceedings)

Abstract
This paper explores the idea to create complex human-like arm movements from movement primitives based on nonlinear attractor dynamics. Each degree-of-freedom of an arm is assumed to have two independent abilities to create movement, one through a discrete dynamic system, and one through a rhythmic system. The discrete system creates point-to-point movements based on internal or external target specifications. The rhythmic system can add an additional oscillatory movement relative to the current position of the discrete system. In the present study, we develop appropriate dynamic systems that can realize the above model, motivate the particular choice of the systems from a biological and engineering point of view, and present simulation results of the performance of such movement primitives. Implementation results on a Sarcos Dexterous Arm are discussed.

link (url) [BibTex]

1998

link (url) [BibTex]


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Robust local learning in high dimensional spaces

Vijayakumar, S., Schaal, S.

In 5th Joint Symposium on Neural Computation, pages: 186-193, Institute for Neural Computation, University of California, San Diego, San Diego, CA, 1998, clmc (inproceedings)

Abstract
Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings requires a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper, we suggest a partial revision of this view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm.

[BibTex]

[BibTex]


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Local dimensionality reduction

Schaal, S., Vijayakumar, S., Atkeson, C. G.

In Advances in Neural Information Processing Systems 10, pages: 633-639, (Editors: Jordan, M. I.;Kearns, M. J.;Solla, S. A.), MIT Press, Cambridge, MA, 1998, clmc (inproceedings)

Abstract
If globally high dimensional data has locally only low dimensional distributions, it is advantageous to perform a local dimensionality reduction before further processing the data. In this paper we examine several techniques for local dimensionality reduction in the context of locally weighted linear regression. As possible candidates, we derive local versions of factor analysis regression, principle component regression, principle component regression on joint distributions, and partial least squares regression. After outlining the statistical bases of these methods, we perform Monte Carlo simulations to evaluate their robustness with respect to violations of their statistical assumptions. One surprising outcome is that locally weighted partial least squares regression offers the best average results, thus outperforming even factor analysis, the theoretically most appealing of our candidate techniques.

link (url) [BibTex]

link (url) [BibTex]


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Constructive incremental learning from only local information

Schaal, S., Atkeson, C. G.

Neural Computation, 10(8):2047-2084, 1998, clmc (article)

Abstract
We introduce a constructive, incremental learning system for regression problems that models data by means of spatially localized linear models. In contrast to other approaches, the size and shape of the receptive field of each locally linear model as well as the parameters of the locally linear model itself are learned independently, i.e., without the need for competition or any other kind of communication. Independent learning is accomplished by incrementally minimizing a weighted local cross validation error. As a result, we obtain a learning system that can allocate resources as needed while dealing with the bias-variance dilemma in a principled way. The spatial localization of the linear models increases robustness towards negative interference. Our learning system can be interpreted as a nonparametric adaptive bandwidth smoother, as a mixture of experts where the experts are trained in isolation, and as a learning system which profits from combining independent expert knowledge on the same problem. This paper illustrates the potential learning capabilities of purely local learning and offers an interesting and powerful approach to learning with receptive fields. 

link (url) [BibTex]

link (url) [BibTex]


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Biomimetic gaze stabilization based on a study of the vestibulocerebellum

Shibata, T., Schaal, S.

In European Workshop on Learning Robots, pages: 84-94, Edinburgh, UK, 1998, clmc (inproceedings)

Abstract
Accurate oculomotor control is one of the essential pre-requisites for successful visuomotor coordination. In this paper, we suggest a biologically inspired control system for learning gaze stabilization with a biomimetic robotic oculomotor system. In a stepwise fashion, we develop a control circuit for the vestibulo-ocular reflex (VOR) and the opto-kinetic response (OKR), and add a nonlinear learning network to allow adaptivity. We discuss the parallels and differences of our system with biological oculomotor control and suggest solutions how to deal with nonlinearities and time delays in the control system. In simulation and actual robot studies, we demonstrate that our system can learn gaze stabilization in real time in only a few seconds with high final accuracy.

link (url) [BibTex]

link (url) [BibTex]


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Towards biomimetic vision

Shibata, T., Schaal, S.

In International Conference on Intelligence Robots and Systems, pages: 872-879, Victoria, Canada, 1998, clmc (inproceedings)

Abstract
Oculomotor control is the foundation of most biological visual systems, as well as an important component in the entire perceptual-motor system. We review some of the most basic principles of biological oculomotor systems, and explore their usefulness from both the biological and computational point of view. As an example of biomimetic oculomotor control, we present the state of our implementations and experimental results using the vestibulo-ocular-reflex and opto-kinetic-reflex paradigm

link (url) [BibTex]

link (url) [BibTex]


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Local adaptive subspace regression

Vijayakumar, S., Schaal, S.

Neural Processing Letters, 7(3):139-149, 1998, clmc (article)

Abstract
Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings requires a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper we suggest a partial revision of the view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique  as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm. 

link (url) [BibTex]

link (url) [BibTex]

1993


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Learning passive motor control strategies with genetic algorithms

Schaal, S., Sternad, D.

In 1992 Lectures in complex systems, pages: 913-918, (Editors: Nadel, L.;Stein, D.), Addison-Wesley, Redwood City, CA, 1993, clmc (inbook)

Abstract
This study investigates learning passive motor control strategies. Passive control is understood as control without active error correction; the movement is stabilized by particular properties of the controlling dynamics. We analyze the task of juggling a ball on a racket. An approximation to the optimal solution of the task is derived by means of optimization theory. In order to model the learning process, the problem is coded for a genetic algorithm in representations without sensory or with sensory information. For all representations the genetic algorithm is able to find passive control strategies, but learning speed and the quality of the outcome are significantly different. A comparison with data from human subjects shows that humans seem to apply yet different movement strategies to the ones proposed. For the feedback representation some implications arise for learning from demonstration.

link (url) [BibTex]

1993

link (url) [BibTex]


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A genetic algorithm for evolution from an ecological perspective

Sternad, D., Schaal, S.

In 1992 Lectures in Complex Systems, pages: 223-231, (Editors: Nadel, L.;Stein, D.), Addison-Wesley, Redwood City, CA, 1993, clmc (inbook)

Abstract
In the population model presented, an evolutionary dynamic is explored which is based on the operator characteristics of genetic algorithms. An essential modification in the genetic algorithms is the inclusion of a constraint in the mixing of the gene pool. The pairing for the crossover is governed by a selection principle based on a complementarity criterion derived from the theoretical tenet of perception-action (P-A) mutuality of ecological psychology. According to Swenson and Turvey [37] P-A mutuality underlies evolution and is an integral part of its thermodynamics. The present simulation tested the contribution of P-A-cycles in evolutionary dynamics. A numerical experiment compares the population's evolution with and without this intentional component. The effect is measured in the difference of the rate of energy dissipation, as well as in three operationalized aspects of complexity. The results support the predicted increase in the rate of energy dissipation, paralleled by an increase in the average heterogeneity of the population. Furthermore, the spatio-temporal evolution of the system is tested for the characteristic power-law relations of a nonlinear system poised in a critical state. The frequency distribution of consecutive increases in population size shows a significantly different exponent in functional relationship.

[BibTex]

[BibTex]